EU leaders rebuffed a plea by Theresa May on Thursday to help her sell her Brexit deal to parliament, warning she must set out exactly what she wants -- and announcing they would step up contingency plans in case the deal collapses.

She told the other 27 leaders the agreement could still pass the House of Commons next month if they helped her reassure lawmakers over a controversial "backstop" clause on Ireland, a British official said.

But European sources said the atmosphere in the room was tense, with German Chancellor Angela Merkel and other leaders repeatedly interrupting May to ask exactly what she wanted.

European Commission president Jean-Claude Juncker told reporters afterwards: "Our UK friends need to say what they want instead of asking us what we want."

He added: "Theresa May has led a courageous fight, but unfortunately we are not seeing the results."

May floated the idea of setting a target date to agree a free trade deal with the EU if one had not been agreed by the end of a post-Brexit transition period, to avoid Britain falling into the backstop.

Many of her MPs fear the arrangement for Britain to enter a temporary customs union with the EU to avoid border checks with Ireland could become permanent.

But European leaders have said they will not accept a time limit, and after May left agreed a statement that the Brexit deal "is not open for renegotiation".

With May having promised to have something to offer MPs before they finally vote on the Brexit deal by January 21, Juncker said she would have to come up with proposals in the next few weeks if she wanted Europe's support.

May told EU leaders they must help her "change the perception that the backstop could be a trap from which the UK cannot escape", adding: "Until we do, the deal -- our deal -- is at risk."

"With the right assurances, this deal can be passed. Indeed it is the only deal that is capable of getting through my parliament," she told them.

But while an early draft of the summit conclusions had said the EU "stands ready to examine whether any further assurances can be provided" on the backstop, this was removed from the final published version.

Juncker did offer one olive branch, promising that talks on the future trading relationship -- a deal on which would undermine the need for the backstop -- would start as soon as MPs and the European Parliament approved the Brexit deal.

The summit statement also confirmed the backstop would only "apply temporarily" and that EU members would work to "conclude expeditiously" the new trade deal.

But this is not the legally binding promise sought by Brexiteers and the Northern Irish party that props up May's government -- without which they have warned they will not support the deal.

Crushing defeat

May arrived in Brussels wounded by a confidence vote in her party on Wednesday night, which she won but in which more than one-third of her MPs voted against her.

The move was sparked by her decision to delay a parliamentary vote on the Brexit deal planned for Tuesday, amid fears of a crushing defeat. It has been delayed to next month.

But ahead of the confidence vote May was forced to confirm she would not fight the next general election planned for 2022.

Instead, she said her focus was on salvaging her plan for an orderly Brexit. Before the EU leaders savaged her plan, she had admitted she did not expect "an immediate breakthrough".

Irish Prime Minister Leo Varadkar, who earlier met with May on the sidelines of the summit, stressed again the backstop must be part of the deal.

"As the EU we are very keen to offer explanations, assurances, clarifications, anything that may assist MPs to understand the agreement, and hopefully to support it. But the backstop is not on the table," he said.